Discretization results for the Huff and Pareto-Huff competitive location models on networks |
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Authors: | Peter H. Peeters Frank Plastria |
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Affiliation: | (1) Department of Management Informatics, Vrije Universiteit Brussel, Pleinlaan 2, B 1050 Brussels, Belgium |
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Abstract: | In this paper we prove that there always exists a finite set that includes an optimal solution for the Huff and the Pareto-Huff competitive models on networks with the assumption of a concave function of the distance. In the Huff model, there is always a vertex of the network that belongs to the solution set. For the Pareto-Huff model, we prove that there is always an optimal solution at, or an ε-optimal solution close to, a vertex or an isodistant point, a new concept introduced in this paper. |
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Keywords: | Competitive location Huff model Pareto-Huff model isodistant point |
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